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A046731 a(n) = sum of primes < 10^n. 18
0, 17, 1060, 76127, 5736396, 454396537, 37550402023, 3203324994356, 279209790387276, 24739512092254535, 2220822432581729238, 201467077743744681014, 18435588552550705911377, 1699246443377779418889494, 157589260710736940541561021, 14692398516908006398225702366 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(21) was already correctly computed by Marc Deleglise in 2009 but in 2011 he withdrew his result because his verification failed. - Kim Walisch, Jun 06 2016
LINKS
Lorenzo Pieri, Table of n, a(n) for n = 0..26 [terms a(0)-a(20) from Marc Deleglise; terms a(21)-a(23) from Kim Walisch; terms a(24)-a(25) from David Baugh]
M. Deleglise and J. Rivat, Computing pi(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method, Math. Comp., 65 (1996), 235-245.
Cino Hilliard, GmpDemo Sumprimes.
Kim Walisch, primesum program.
FORMULA
a(n) is about 100^n/(n log 100). - Charles R Greathouse IV, Jan 29 2013
a(n) = Sum_{i=2..10^n} A061397(i). - José de Jesús Camacho Medina, Aug 08 2016
EXAMPLE
The primes less than 10 give 2+3+5+7 = 17.
MATHEMATICA
Join[{0, s = 17}, Table[Do[If[PrimeQ[i], s += i], {i, 10^n + 1, 10^(n + 1), 2}]; s, {n, 7}]] (* Jayanta Basu, Jun 28 2013 *)
Table[Sum[Prime[i], {i, PrimePi[10^n]}], {n, 0, 7}] (* Kim Walisch, Dec 21 2017 *)
PROG
(PARI) a(n) = my(s=0); forprime(p=1, 10^n, s += p); s; \\ Michel Marcus, Jan 14 2015
(Perl) use ntheory ":all"; say "$_ ", sum_primes(10**$_) for 0..15; # Dana Jacobsen, May 04 2017
CROSSREFS
Cf. A034387.
Sequence in context: A221343 A221376 A077645 * A221268 A179157 A130449
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Corrected and extended by Jud McCranie
a(12) and a(13) from Cino Hilliard, Aug 14 2006
New value for a(13) from Cino Hilliard, Oct 24 2007
There was indeed an error in a(13) both in the entry here and in the b-file. This has now been corrected. - N. J. A. Sloane, Nov 23 2007
Two new values from Marc Deleglise, May 21 2008 - see the b-file.
a(21) from Marc Deleglise, Jun 29 2008 - see the b-file.
Nov 15 2011: Marc Deleglise has withdrawn his value for a(21).
a(21)-a(22) from Kim Walisch, Jun 06 2016
a(23) from Kim Walisch, Jun 11 2016
a(24) from David Baugh using Kim Walisch's primesum program, Jun 17 2016
a(25) from David Baugh using Kim Walisch's primesum program, Oct 16 2016
a(26) from Kim Walisch, May 25 2022, added by Lorenzo Pieri
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)